Method and Apparatus for Constructing Fast Converging Polar Codes with Belief Progapation Decoder

1. A method for constructing a fast converging polar code based on a belief propagation decoder at a transmitter node of a network to propagate messages through channels of the network to a receiver node, the method comprising: analyzing decoding importance for each individual bit of an initial belief propagation decoder in channels of the network via an analysis unit of a fast converging polar code construction apparatus of the belief propagation decoder, wherein the analyzing includes determining a degree of contribution to decoding a message propagation by each individual bit, the decoding performed by the initial belief propagation decoder, and generating an index including index values corresponding to the degree of contribution of each individual bit to decoding the message propagation; reconstructing the polar code depending on an analyzing result using the individual bit having the highest index value from the index via a processing unit of the fast converging polar code construction apparatus; and applying the reconstructed polar code to provide error correction for data in the channels of the network via the belief propagation decoder; and propagating a message decoded using the reconstructed polar code from the transmitter node of the network to the receiver node over the channels of the network.

2. The method of claim 1, wherein the analyzing includes: analyzing decoding importance between individual nodes within an individual polarization kernel in a belief propagation decoding process at an initial iteration of a number of iterations of the initial belief propagation decoder.

3. The method of claim 1, wherein the analyzing includes: analyzing the degree of contribution of a message through a codeword bit stage and a message bit stage, in a belief propagation decoding process at an initial iteration of a number of iterations of the initial belief propagation decoder.

4. The method of claim 3, wherein the reconstructing includes: additionally transmitting a bit having the highest index value by removing a bit having a lowest index value from among all codeword bits through puncturing for removing some of the codeword bits and extending for transmitting an additional bit and allocating a degree of freedom, which is secured to produce a secured degree of freedom by removing the bit having the lowest index value, to the bit having the highest index value.

5. The method of claim 4, wherein the reconstructing includes: maintaining a structure of the polar code by allocating the secured degree of freedom to the bit having the highest index value.

6. A method for constructing a fast converging polar code based on a belief propagation decoder at a transmitter node of a network to propagate messages through channels of the network to a receiver node, the method comprising: analyzing decoding importance between individual nodes within an initial belief propagation decoder in channels of the network via an analysis unit of a fast converging polar code construction apparatus of the belief propagation decoder, wherein the analyzing includes determining a degree of contribution for each individual node in a belief propagation decoding process performed on a message propagation at an initial iteration of a number of iterations of the an initial belief propagation decoder, wherein each individual node has a codeword bit, and wherein an index value for each codeword bit is generated based on a degree of contribution of the individual node to decoding the message propagation; and reconstructing the polar code depending on an analyzing result via a processing unit of the fast converging polar code construction apparatus,, wherein the reconstructing prioritizes a kernel having the highest index value; and, applying the reconstructed polar code to provide error correction for data in the channels of the network via the belief propagation decoder; and propagating a message decoded using the reconstructed polar code from the transmitter node of the network to the receiver node over the channels of the network.

7. The method of claim 6, wherein the analyzing includes: analyzing the degree of contribution of a message through a codeword bit stage and a message bit stage, in the belief propagation decoding process at an initial iteration of the number of iterations of the initial belief propagation decoder.

8. The method of claim 7, wherein the reconstructing includes: additionally transmitting a bit having a highest index value by removing a bit having a lowest index value from among all codeword bits through puncturing for removing some of the codeword bits and extending for transmitting an additional bit and allocating the degree of freedom, which is secured by removing the bit having the lowest index value, to a bit having the highest index value.

9. The method of claim 8, wherein the reconstructing includes: maintaining a structure of the polar code by allocating the secured degree of freedom to the bit having the highest index value.

10. An apparatus for constructing a fast converging polar code based on a belief propagation decoder in channels of a network between nodes of the network, comprising: an analysis unit configured to analyze decoding importance for each individual bit of an initial belief propagation decoder, wherein the analyzing includes determining a degree of contribution to decoding a message propagation by each individual bit, the decoding performed by the initial belief propagation decoder, and generating an index including index values corresponding to the degree of contribution of each individual bit to decoding the message propagation; a processing unit configured to reconstruct the polar code depending on an analyzing result using the individual bit having the highest index value from the index; and a communication device applying the reconstructed polar code to provide error correction for data in the channels of the network, the channels propagating a message decoded using the reconstructed polar code between a transmitter node and a receiver node of the network.

11. The apparatus of claim 10, wherein the analysis unit analyzes decoding importance between individual nodes within an individual polarization kernel in a belief propagation decoding process at an initial iteration of a number of iterations of the initial belief propagation decoder.

12. The apparatus of claim 10, wherein the analysis unit analyzes the degree of contribution of a message through a codeword bit stage and a message bit stage, in a belief propagation decoding process at an initial iteration of a number of iterations of the initial belief propagation decoder.

13. The apparatus of claim 12, wherein the processing unit additionally transmits a bit having a highest index value by removing a bit having a lowest index value from among all codeword bits through puncturing for removing some of the codeword bits and extending for transmitting an additional bit and allocating the degree of freedom, which is secured to produce a secured degree of freedom by removing the bit having the lowest index value, to a bit having the highest index value.

14. The apparatus of claim 13, wherein the processing unit maintains a structure of the polar code by allocating the secured degree of freedom to the bit having the highest index value.

15. A method for constructing a fast converging polar code based on a belief propagation decoder in channels of a network between nodes of the network, the method comprising: analyzing decoding importance for each individual bit of an initial belief propagation decoder via an analysis unit of a fast converging polar code construction apparatus of the belief propagation decoder by analyzing the degree of contribution of a message through a codeword bit stage and a message bit stage, in a belief propagation decoding process at an initial iteration of a number of iterations of the initial belief propagation decoder, wherein the analyzing includes determining a degree of contribution to decoding propagation of the message by each individual bit, and generating an index including index values corresponding to the degree of contribution of each individual bit to decoding the message propagation; and reconstructing the polar code depending on an analyzing result using the individual bit having the highest index value from the index via an analysis unit of a fast converging polar code construction apparatus of the belief propagation decoder; and applying the reconstructed polar code to provide error correction for data in the channels of the network; and propagating a message decoded using the reconstructed polar code from the transmitter node of the network to the receiver node over the channels of the network.